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COMBINATORIAL DEPLETION · 2D · RANK-6 · 75% DEPTH

2-Deck Six-Pip Card Depletion at 75% Penetration (4% Audit DEP151)

Removing 7 of 8 Six-Pip Card (Rank-6) cards at 75% penetration of a 2-deck (104-card) shoe leaves 1 Rank-6 cards inside a 26-card stub (DEP151), producing 45.8947% Banker wins, 44.5728% Player wins, 9.5325% Ties, and a 0.5140% Banker house edge under 4%.

Banker EV (4% Vig)
-0.5140%
Player EV (1:1)
-1.3218%
Rank-6 in 26-Card Stub
1/8
Single-Hand Std Dev
0.9388
Engine-Verified Scoreboard · 18 Hands

Read the Board at Table Speed

Open this shoe in /calculator
Big Road B B P P B B P B P B P P B B P P B P
Big Eye Boy = = = = ≠ = = = ≠ ≠ = = = = ≠
Small Road = = ≠ ≠ = = ≠ ≠ ≠ ≠ = = ≠
Cockroach Pig ≠ ≠ ≠ = ≠ ≠ ≠ ≠ ≠ ≠ ≠

Reference shoe scoreboard (BBPPBBPBPBPPBBPPBP) illustrating derived-road symmetry checks alongside DEP151 (2D Rank-6 at 75% depth).

Big Road B is Banker, P is Player Roads under it Red (=): repeating Blue (≠): breaking
Step-by-Step Mark Proofs (Rule 1 & Rule 2)
Big Eye Boy Mark #2

Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 3 starts, so use Rule 1: compare Column 2 with Column 1, 1 column further back.
  2. Column 2 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 2, the one that just finished, with Column 1.

Small Road Mark #2

Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

  1. Column 4 starts, so use Rule 1: compare Column 3 with Column 1, 2 columns further back.
  2. Column 3 has 2 beads. Column 1 has 2 beads. Same depth → red (=).

Common table reading watchout: Comparing the wrong columns. Compare Column 3, the one that just finished, with Column 1.

Cockroach Pig Mark #2

Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

  1. Column 6 starts, so use Rule 1: compare Column 5 with Column 2, 3 columns further back.
  2. Column 5 has 1 bead. Column 2 has 2 beads. Different depth → blue (≠).

Common table reading watchout: Comparing the wrong columns. Compare Column 5, the one that just finished, with Column 2.

Verified Reference Data

Key Facts & Table Specifications

Stub Size (DEP151)
26 / 104 Cards

75% penetration depth in 2D (double-deck European salon privé carriers and two-deck shoe pits).

Rank-6 Remaining
1 of 8 Cards

7 6-pip cards (standing threshold and Banker 6 trigger) removed from the 2D pack.

Banker EV (4% Vig)
-0.5140%

Resolved at 45.8947% Banker win rate under 4% settlement.

Player EV (1:1)
-1.3218%

Resolved at 44.5728% Player win rate with 0.9388 unit standard deviation.

Tie Incidence (8:1)
9.5325%

Produces a 14.2074% house hold on the 8-to-1 Tie wager in state DEP151.

FINITE-SHOE ENUMERATION · DEP151

How Six-Pip Card Depletion at 75% Depth Impacts 2D (4% Vig)

Removing 7 of 8 Rank-6 cards by the 75% mark of a 2-deck shoe (DEP151, 26 cards left) leaves 1 Six-Pip Card cards and adjusts conditional probabilities to 45.8947% Banker, 44.5728% Player, and 9.5325% Tie under 4%.

Comparing initial 104-card 2D weights against stub DEP151 (26 cards, 75% depth, 1 Rank-6 left) illustrates how banker 6 only draws (dep151) when player pulls a third-card (2d-75%) 6 or 7; depleting 6s (dep151·2d-75%) directly alters both banker 6 draws and super 6 settlement frequency (-1.13 bps slope, 0.5140% 4% Vig edge).

State DEP151 (2D, 75% depth, 1/8 Rank-6 left, 4% Vig)
Wager / MetricState DEP151 Value2D BaselineSettlement Note
DEP151 Banker (4% Vig)45.8947% (-0.5140% EV)45.8998%DEP151 2D 75% (1 Rank-6)
DEP151 Player (1:1)44.5728% (-1.3218% EV)44.5676%DEP151 26-card 2D stub (0.9388 SD)
DEP151 Tie (8:1)9.5325% (-14.2074% EV)9.5326%DEP151 Rank-6 (7 out, 1 in)
TABLEAU & SCOREBOARD SEPARATION · DEP151

Third-Card Tableau Sensitivity vs Derived-Road Marks (DEP151 · 2D)

On the electronic scoreboard for DEP151 (2D, 75% depth, 26 cards left), Bead Plate and Big Road circles record Banker (45.8947%) and Player (44.5728%) outcomes, whereas Big Eye Boy, Small Road, and Cockroach Pig marks reflect column symmetry rather than Rank-6 card counts (1/8).

  • DEP151 (2D 75%): 26/104 cards with 1/8 Rank-6 (4A).
  • DEP151 (Rank-6 split): 45.8947% Banker, 44.5728% Player, 9.5325% Tie in 26 2D cards (4B).
  • DEP151 (4% Vig EV): -0.5140% Banker, -1.3218% Player, -14.2074% Tie, 0.9388 SD at 75% (4C).
  • DEP151 (2D roads): red/blue marks log Big Road columns, never 1 Rank-6 stub count (4D).
Table Reality Check

Myth vs. Truth

MythWhen 7 Six-Pip Card cards leave a 2D shoe by 75% depth (DEP151), Big Eye Boy red or blue marks show whether Banker or Player will win next.
TruthDerived-road red and blue marks only compare Big Road column lengths and never track Rank-6 stub counts (1/8 in 26 cards); Banker carries a -0.5140% expectation under 4%.
6 modules · 36 lessons · $25/month · Module 1 (10 lessons) free

Read Every Derived Road at Table Speed

Every reference guide, glossary definition, and road calculator on Baccarat Smart is open for everyone. When you want all 6 modules and 36 lessons (about 5.5 hours of lessons) organized in structured step-by-step order with 74 hands-on boards, 94 quiz checks along the way, and Cloud Shoe Log sync across web, iPhone, and Android, start Module 1 (10 lessons, about 64 minutes of lessons) free or unlock full membership for $25 a month.

  • Structured step-by-step track across Foundations, Big Eye Boy, Small Road, and Cockroach Pig
  • 74 interactive lesson scoreboards and 94 inline quiz checks with plain-English mark feedback
  • Cloud Shoe Log and cross-device progress on web, iOS, and Android